Confidence intervals based on cluster-robust covariance matrices can be constructed in many ways. In addition to conventional intervals obtained by inverting Wald (t) tests, the paper studies intervals obtained by inverting LM tests, studentized bootstrap intervals based on the wild cluster bootstrap, and restricted bootstrap intervals obtained by inverting bootstrap Wald and LM tests. It also studies the choice of an auxiliary distribution for the wild bootstrap, a modified covariance matrix based on transforming the residuals, which was proposed previously, and modified wild bootstrap procedures based on the same idea, which are new. Some procedures perform extraordinarily well even with the number of clusters is small.
wild bootstrap auxiliary distribution CRVE cluster-robust inference studentized bootstrap